Disequilibrium Econometrics on Micro Data - Caltech Authors

Disequilibrium Econometrics on Micro Data Author(s): M. B. Bouissou, J. J. Laffont and Q. H. Vuong Source: The Review of Economic Studies, Vol. 53, No. 1 (Jan., 1986), pp. 113-124 Published by: Oxford University Press Stable URL: http://www.jstor.org/stable/2297595 Accessed: 20-09-2017 23:27 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms

Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to The Review of Economic Studies

This content downloaded from 131.215.23.153 on Wed, 20 Sep 2017 23:27:14 UTC All use subject to http://about.jstor.org/terms

Review of Economic Studies (1986) LIII, 113-124 0034-6527/86/00080113$02.00

? 1986 The Society for Economic Analysis Limited

Disequilibrium Econometrics on Micro Data M. B. BOUISSOU J. J. LAFFONT

Universite des Sciences Sociales, Toulouse and

Q. H. VUONG California Institute of Technology

This paper brings some empirical evidence to the construction of a more disaggregated view

of disequilibrium. Individual data on firms collected by INSEE through periodic Business Surveys are used to construct the distribution of firms over the four possible disequilibrium regimes. Then

the behavior of this distribution over time is analyzed by estimating dynamic conditional logit models on panel data.

The breakthrough paper on disequilibrium econometrics (Fair and Jaffee (1972)) is now more than ten years old. Quandt (1982) has recently surveyed the development of the econometric methods dealing with the particular non-linear models generated by fix-price

models. Laffont (1983) has summarized and discussed the main estimation results of macro-disequilibrium models. Though these empirical results are interesting, they suffer from an excessive aggregation which prevents a sufficiently precise discussion of the

nature of unemployment (classical unemployment vs. Keynesian unemployment) and of the appropriate corrective economic policies. The purpose of this paper is to bring some empirical evidence to the construction

of a more disaggregated view of disequilibrium by using individual data on firms collected

by the Institut National de la Statistique et des Etudes Economiques (INSEE) through

periodic Business Survey Tests.' A great potential of this more disaggregated approach is the ability to study the relative shares of classical and Keynesian unemployment. For

policy purposes it is also important to explain why a given sector is in one type of unemployment or the other. The paper is organized as follows. Section 1 presents the data and describes how

the indicator of the regime in which a firm is can be constructed from the firm's answers

to the INSEE surveys. The resulting distribution on the sample of firms over the four possible disequilibrium regimes is then discussed. Section 2 presents some general remarks on the estimation of conditional logit models on panel data as well as on the general

form of the models that we propose to estimate. Section 3 studies the dynamics of the regime distribution by introducing the explanatory variables suggested by micro-disequili-

brium models (see Muellbauer (1978), Malinvaud (1981), Kooiman (1982)). Section 4 concludes the paper.

1. DESCRIPTION OF DATA AND CONSTRUCTION OF VARIABLES

This section presents the data that are used in our empirical analysis. 113


114 REVIEW OF ECONOMIC STUDIES la. Individual data

Our micro data has been collected by INSEE from about 4000 firms through periodic

Business Survey Tests.2 These Survey Tests were taken three times a year (in June, November, and March) from June 74 to June 78, and four times a year (in June, October, January, and March) from June 78 to June 82. Only firms with a single major product are retained in the sample. Each firm was also classified according to the nature of its product into one of the following five sectors: 1. Agricultural and Food Industries, 2. Intermediate Goods, 3. Professional Equipment,

4. Automobile, Transportation, 5. Consumption Goods.

From the firm's answers to these surveys, two qualitative variables were constructed:

(i) an indicator of surprise with respect to the demand received by the firm for its product, and (ii) an indicator of the regime experienced by the firm during the period. The demand surprise indicator, denoted MSD, is constructed from the answers to the following questions appearing in each survey:

"Indicate the probable change in demand for your product until the next survey: increasing, stable, decreasing."

"Indicate the change in demand for your product since the last survey: increasing, stable, decreasing." From two successive surveys, we can readily define the variable MSD as:

MSD= 1 if the firm has over-evaluated its demand, MSD = 2 if the firm has correctly evaluated its demand,

MSD = 3 if the firm has under-evaluated its demand.4 Let us now turn to the construction of the regime indicator IR. In the spirit of micro-disequilibrium models we are reasoning as if each firm has its local product market and its local labour market. Let IQ and IL be respectively the indicators of the states of the goods market and of the labour market, where: IL = 1 if excess supply of labour,

IL = 2 if excess demand for labour,

IQ= 1 if excess supply of good,

IQ = 2 if excess demand for good. Information on the indicators IQ and IL can be obtained from the INSEE surveys

since in these surveys firms are asked questions about their perceived constraints on their product and labour markets. Specifically, the indicator IQ is obtained from the answer to the question:

"If you received more orders could you produce more with your actual means?"

If the firm answers YES we presume, following Malinvaud's remark (1980, p. 73), that the firm is constrained on its good market (IQ = 1), while if the firm answers NO we

presume that the firm is not constrained on its good market (IQ = 2). Similarly, the indicator IL is obtained from the answer to the question:


BOUISSOU ET AL. DISEQUILIBRIUM MICRO ECONOMETRICS 115 "Do you now have difficulties in recruiting?"

If the firm answers YES, we presume that it is constrained on its labour market (IL = 2), while if the firm answers NO we presume that it is not constrained on its labour market

(IL= 1). There are obviously some problems with the interpretation to give to these answers; however, various alternative ways of using the answers to the INSEE surveys do not

change the qualitative features of the empirical results presented in Section 3.5 Provided that a firm's answers to both of these questions are available it is possible to classify that firm in one of four possible disequilibrium regimes. Specifically, IR = 1 (Keynesian Unemployment) if IQ = 1 and IL= 1,

IR = 2 (Under Consumption) if IQ = 1 and IL= 2, IR = 3 (Classical Unemployment) if IQ = 2 and IL= 1, IR = 4 (Repressed Inflation) if IQ = 2 and IL = 2. According to this definition of the regime indicator we obtain Table I, which presents

for the whole sample the distribution of the firms over the four possible disequilibrium regimes. These results can be compared with the ex post probabilities of the different regimes obtained by Artus, Laroque, and Michel (1984). One major feature of their

TABLE I

All five sectors Keynesian Under Classical Repressed unemployment consumption unemployment inflation

Date

Sample 1741

(%)

67-03

(%)

(%)

75

03

75

06

75

11

1869

68-27

14-87

11-40

5-46

76

03

1842

62-81

18-24

11-67

7-28

76

06

1787

51-82

22-50

13-43

12-25

76

11

1829

55-28

20-78

13-72

10-22

77

03

1923

57-88

18-82

14-30

9

77

06

1917

58-53

18-62

14-45

8-40

1818

15-51

(%)

69-70

15-51

11-77

5-69

9-79

5-00

00

77

11

2119

60-97

18-12

13-07

7-84

78

03

2013

62-49

18-33

12-57

6-61

78

06

2031

59-87

18-07

14-33

7-73

78

10

1785

60-62

17-54

14-73

7-11

79

01

2036

60-95

16-85

15-28

6-92

79 79

03 06

1988 1965

60-82 56-69

15-79 15-98

16-35 18-73

8-60

79

10

1996

54-61

16-33

20-14

8-92

80

01

1919

56-70

16-21

18-86

8-23

80

03

2031

54-01

16-45

20-38

9-16

80

06

1957

56-11

16-09

18-65

9-15

80

10

2015

63-23

16-63

14-14

6-00

12-42

3-94

7

04

8101

1804

69-01

14-63

8103

1726

71-55

12-57

12-34

3-54

8106

1671

73-55

11

19

11-85

3-41

8110

1774

70-97

12-63

12-91

3-49

82

01

1832

70-69

11-68

13-37

4-26

82

03

1743

69-31

13-42

12-79

4-48

82

06

1648

63-96

15-53

14-93

5-58


116 REVIEW OF ECONOMIC STUDIES

results is obtained here: namely, the predominance of the Keynesian unemployment regime.6

It would be interesting to comment in detail on Table I in the light of the French experience over the period 1975-1982. We shall only mention two important attempts that were made during this period to decrease unemployment with usual Keynesian policies: the Chirac experiment from June 1975 to June 1976 and the Mauroy experiment from June 1981 to June 1982. Both share the same features: a strong decline in the proportion of firms in the Keynesian unemployment regime with an increase in all other regimes. The Mauroy experiment appears less effective with a stronger relative increase in the proportion of firms in the classical unemployment regime. This is not surprising

given that in the Mauroy experiment the low real wages have been increased substantially. Note also the dynamics after the Chirac experiment. The proportion of firms in the

Keynesian unemployment regime increases again, but the proportion of firms in the classical unemployment regime continues to increase. Finally, the substantial increase in Keynesian unemployment from June 1980 to January 1981 seems to be due to the second oil crisis.

The same classification was carried out for each sector of the economy. In particular we found that the intermediate goods sector and professional equipment sector are the

slowest to react; the automobile and transportation sector reacts quite strongly and rapidly; the consumption good sector reacts quickly but not as strongly.

lb. Macro data

Some macroeconomic variables are used as additional explanatory variables (see Muellbauer (1978), Malinvaud (1981), and Kooiman (1982)). All the macroeconomic variables were dichotomized and constructed from appropriate series obtained from the Comptes

Nationaux Trimestriels published by INSEE for the period under study. If IX denotes

the dichotomous variable associated with the latent continuous variable X, then the dichotomization rule is:

IX =1 if X is above a trend,

IX = 2 if X is below a trend, where the trend is obtained by adjusting a line on the time series X. Two sectoral indicators and two national indicators were constructed in this way. These are:

IGS: indicator of sectoral public expenditures, IGT: indicator of total public expenditures,

ISB: indicator of the sectoral real cost of labour as measured by real gross wages, which include employer and employee social security

payments and the like, ISN: indicator of purchasing power as measured by real take-home pay, which includes personal income taxes for the whole economy.7


BOUISSOU ET AL. DISEQUILIBRIUM MICRO ECONOMETRICS 117

In addition, lags of these indicators are also used as explanatory variables. Specifically, if IX is an indicator, then IX1 is the indicator lagged 3 months,

IX2 is the indicator lagged 6 months, IX3 is the indicator lagged 9 months.

2. ESTIMATION OF DYNAMIC CONDITIONAL MODELS ON PANEL DATA

All the models that we estimate are conditional logit models (see e.g. McFadden (1974), Nerlove and Press (1973, 1976)) where the endogeneous variable is the disequilibrium regime indicator IR. As a matter of fact, we consider a special case of the conditional logit model since all our explanatory variables are qualitative. All our models are dynamic in the sense that they all include the 3 months lagged

regime indicator IR1 as an explanatory variable. Thus we can think of the remaining explanatory variables as explaining the 3 months transition probability from one regime to another. Our models are therefore of the form: IRIIRl, IA, IB,...

where IA, IB, . . . are explanatory variables to be defined in Section 3. The parameterization

used is the ANOVA parameterization (see Nerlove and Press (1976), Vuong (1982)). As usual we restrict the effect of each explanatory variable to its bivariate effect. Specifically,

let IRit, IAit, IBit,... denote the regime and the explanatory variables for the i-th firm at time t respectively. Let KR, KA, KB, . . . denote the number of categories of these variables

where, in our case, KR is equal to 4, KA and KB are equal to either two or three. Then we have:

log Pr (IRit = k IIR 1 t IAit IBit, . . A. + ak +11kllIlt KA

+Yai 3k,aDa(IAit)

+EK-13k,bDb(IBit)+ (l where D (IXit) is equal to one if IXit = x, and zero otherwise, the parameters a and ,3 satisfy the ANOVA constraints: KR

k-1 ak 0,

Ek=R Bkx EKx1 13k,x =0, Vx, Vk, (2) and ,u is a normalizing parameter depending only on the a 's and 13's so that, given IR lit,

IAi,, IBit,..., the conditional probabilities in (1) add up to one.8 Conditional logit models have been in general estimated on cross-section data only. The reason is that estimation of such models relies on the usual assumption that the

observations are mutually independent, an assumption that is hardly justified in time series or panel data. Since we are ultimately interested in the effects of macro indicators such as IGT that therefore do not vary across individuals, it is necessary to use panel data in order to identify these macro effects. In this section we justify our estimation procedure on theoretical grounds. As a matter of fact, our justification is valid for the



estimation of any dynamic conditional model on panel data when macro explanatory variables are possibly present.

Suppose that one has available a complete panel data on T equally spaced periods

(t= 1, .. ., T) for n individuals (i= 1, ..., n). Let Yi, be the endogenous random able(s) observed at time t for the ith individual. Let Xi, and Z, be vectors of ex variables where Xi, vary across individuals while Zt do not. For instance, Xi, m IR1 or MSD, while Zt may be IGT or IGS.

Let Y', be the set of variables { Yis, YiS+1,..., YiJ where s -t. We ma following assumptions:

Assumption A.1 (Markov Specification). For any i= 1, ..., n, and any t=

h+1l,...,I T:

Pr(Y tIYt-,1 Xt, Ztoo) = Pr (Yj YitYh, Xit-h, Zt-h) where Pr (AIB) is the conditional density of the variables in A given the variables in B, and h is the maximum lag specified. It is assumed that h < T. Given the choice of a family (in general parametric) of conditional distributions,

Assumption A.1 is nothing else than the specification of a Markovian structure of order h.

Assumption A.2 (stability). (a) For any i = 1, .. ., n, and any t, s in {h + 1,..., T}:

Pr (Y Ylt h, Xt-h, Zt-h)= Pr (YiI Yisl Y hs-h, Zsh), (b) For any i, j in {1, ... ., n}, and any t = h + 1, .. ., T: Pr (Yit YI1 h, Xft-h, Zt-h) = Pr (Yjtl Yt 1h, Xt-h, Zt h)Assumptions A2(a) and A2(b) respectively require that the conditional model of interest be stable across time and across individuals. Clearly some stability assumptions, which may not be as strong, are needed in order to estimate a model. The next assumption deals with the sampling of individuals.

Assumption A.3 (Sampling). The n stochastic vector processes {( Yit, Xit); t = -oo, T} for i = 1, .. ., n are mutually independent given the stochastic process {Zt; t = -oc, T}, i.e. for any i:

( Yi_00 Xioo){( J _00, XJ,_00); j 0 i}|ZTX

where AIBIC denotes that A and B are conditionally independent given C.

For instance, if there are no macro variables Zt, then Assumption A.3 simply means that the sampling of individuals is random. Assumption A.4 (Exogeneity). For any i=1,..., n, and any t=1, .. ., T:

X+?Z+?? ytt+ I tl t0 If there are no macro variables Zt, then Assumption A.4 simply requires that Yit does not Granger cause Xi, or equivalently that Xit is strictly exogeneous to Yit (see Chamberlain (1982), Bouissou, Laffont, and Vuong (1985)). Assumptions A.1 to A.4 can be considered as the standard assumptions underlying the estimation of a dynamic conditional model on panel data.9 It is worth noting that we obtain as a special case (h = 0, T = 1) the assumptions that are implicit in the estimation


BOUISSOU ET AL. DISEQUILIBRIUM MICRO ECONOMETRICS 119 of a conditional model on a cross section, and as another special case (n = I) the

assumptions that justify the estimation of a conditional model on time series. We now consider the likelihood function associated with the observations on the

panel { Yit, Xit, Zt; i = 1, . . ., n, t = 1, . . ., T}. Since h may not be null, we shall in fact consider the conditional likelihood function Lyxz given all the variables prior to period h+l, i.e.

Lyxz = Pr [(( YThl XiThl); i = 1, ... , n), Zh+11(( Y Xv); i-1,..., n), Z_0,]We have:

Lyxz = Lylxz x Lxz with

Lylxz = Pr [(YTh+l; i-1,..., n)|(( Yh_O, XT i); i = 1,..., n), Z_OO] (3) Lxz= Pr [(Xih+l; i 1,*.., n), Zh+?1(( _ Xi ); i = 1,..*, n), Z_o] (4) Since Lyxz is the (conditional) likelihood for (((YTh+l, XTh+l); i =1,..., n), ZT+1) and since Lxz is the (conditional) likelihood for ((XTh?l; i= 1,..., n), ZT?D, it follows

that Lylxz as defined in (3) is the conditional likelihood for (YTh?l; i = I,..., n) given ((XT h+l; i = 1,..*, n), ZT+1). We have: T

Lylxz = fl Pr [(Yfit; i = 11 .. I n)|I(( Y'i _10, Xl;_) i =1 ..., In), Z_0O t=h+l

n T

- H H Pr [YitJ Yjt,-j XT,-oo); Z ., n,, ZI0 i=1 t=h+l

n T~ ~ ~~~~Z

n T

rTn flPr Iylyt I-l XT zT 1

i=1 t=h+l

= H H Pr [YJ Y~~~~~~~~~~~~~~~~~~~~~~~~~~2X~~~~~0, X1, Z2O

n

T

-l fl rLlitly-,i i-(i,-(:O9-00J i=l t=h+i

where the first equation is an identity, the second and third equations follow from Assumption A.3, and the fourth equation from Assumption A.4. Moreover, it follows from Assumption A.1 that: n

Lyz

T

-=

i=1 t=h+l

H

H

Pr

[

Yit

Yt

7h,

and from Assumption A.2 that: n

T

yx=H H Pr [Y= Y YilhlY=t-h Xh = Xt-h, Z0h=Zt-h] (5) i=1 t=h+l

where yi,, y h,,, XIt-h, zt-h are the observed realizations of th i,t-h, Xtt-h, Zt-h, and Y, Y', Xo, Z? are the random variable the stability Assumption A.2.

Each of our conditional logit models is estimated by maximizing a conditional likelihood function of the form (5) where the conditional probabilities are defined by

equation (1) and the parameters are the a's and 18's which satisfy the ANOVA constraints (2). From the general properties of conditional maximum likelihood estimation (see



Anderssen (1973), Vuong (1983)) it follows that this procedure leads to consistent

estimates. It is also worth noting from Equation (5) that the conditional likelih

is written as if all the observations were independent where one observation is an

observation on a firm at a given period. In addition Equation (5) shows that we can pool all these n ( T - h) observations.

3. DISEQUILIBRIUM DYNAMICS

Our purpose is to explain using the variables that were mentioned in Section 1 the transition matrix associated with the four possible disequilibrium regimes (see Equation (1)). Specifically, we consider the transition probability from one state to another 3 months later. We have then considered only the dates for which a survey was available

3 months earlier. These dates are 7506, 7606, 7706, 7806, 7901, 7906, 8001, 8006, 8101, 8106, 8201, and 8206 (see Section 1). The number of observations in each sector, where an observation corresponds to a firm for a given date, is: Sector 1: 1241 observations, Sector 2: 4885 observations, Sector 3: 2302 observations, Sector 4: 449 observations, Sector 5: 5293 observations. The transition matrix for the whole industry has the form: KU

UC

CU

RI

p(l/ 1) p(1/2) p(1/3) p(1/4)1 KU p(2/1) p(2/2) p(2/3) p(2/4) UC

p(3/1) p(3/2) p(3/3) p(3/4) CU p(4/1) p(4/2) p(4/3) p(4/4) RI

where p (j/ k) denotes the transition probability from state tions pooled over the 12 periods that were singled out above we can obtain the following observed three-month transition matrix for the whole industry with probabilities given as percentages:

85-82 24-69 24.31 12.13 7 00 64-24 2-74 18-53

5.73 2-32 65-45 14-51 1-45 8-74 7-51 54.84]

There is for each regime a high probability of staying in the same regime. Moreover,

the Keynesian unemployment regime appears to be an absorbing state. Similar characteristics are obtained when transition probabilities are computed for each sector. These qualitative features must, however, be treated with care since the transition probabilities are influenced by some macroeconomic variables that were not invariant over the period under study.

Table II presents a first set of estimation results that were obtained by using only

the lagged regime indicator IR1 and the individual demand surprise indicator MSD.10 These results should be read as follows. When the upper tail probability (UTP) is larger than 5% it means that the current model cannot be rejected against the correspond-

ing unconstrained (or saturated) model by a log-likelihood ratio test at the 5% significance


BOUISSOU ET AL. DISEQUILIBRIUM MICRO ECONOMETRICS 121 level.11 The number below an explanatory variable is the UTP in % of the chi-square Wald statistic that is used to test that the variable is significant. If this number is less

than 5 it means that the suppression of the effect is rejected at the 5% significance lev When an explanatory variable other than IR1 is significant at the 5% level we give for the first category of that variable (IX = 1) the signs of the effects on the four disequilibrium

regimes.'3 For instance, (+, + -, 0) means that an over evaluation in demand (MSD = 1) relatively increases the probabilities of being in regimes 1 and 2, decreases the probability of being in regime 3, and has no significant effect on the probability of being in regime 4 ceteris paribus. TABLE II

Model IR/IR1, MSD IR

IR

1

MSD

UTP

Secto 1

2

3 4

0%

18%

0%

0% 0%

10-70%

(+,0,o,0) 0% 5-53% 0%

87-80%

44.8%

29-80%

(0,0,0,0)

5

0%

0%

24-00%

As expected from the observed transition matrices given above, we find that the lagged regime indicator IR 1 is strongly significant for every sector. We also observe that

the demand surprise indicator is strongly significant for sectors 2, 3, and 5, while it is

not for sectors 1 and 4. Sector 1 (Agricultural and Food Industries) always gave poor results and we shall abstain from giving any explanation. On the other hand, the non-significance of the demand surprise indicator in sector 4 (Automobile and Transportation) is probably due to the predominance of production to orders in this sector. Finally, when the demand surprise indicator is significant it has the "correct" signs. By "correct" signs we mean that when a firm has over-evaluated its future demand, this increases its probability of being in the excess supply (of good) regimes (IR = 1, IR = 2) and decreases

its probability of being in the excess demand (of good) regimes (IR = 3, IR = 4). For our second set of results, we introduce the macroeconomic variables that are suggested by the disequilibrium microeconomic literature and described in Section 1. We only give the main results for each sector. SECTOR 2

Intermediate goods

IR

IR1 MSD IGS 0% 0% 81% 0%

ISB

UTP=6-43%

(+,+,-,-) (-,o,o,+) IR

IR1 MSD IGS IGS1 IGS2 IGS3 UTP= 0% 0% 57% 0% 0% 10%

5-45%

(+,+,-,-) (+,0,0,-) (-,o,0,+) IR IR1 MSD IGT IGT1 IGT2 IGT3 UTP=21 20% 0%

0%

25%

5-46%

1-31%

15%

(+,+-,-) A(0,-,0,0) (-,0,+,0)



In this sector a stimulus on total public expenditures has after 6 months (IGT2) the expected effect of decreasing the probability of being in the Keynesian unemployment regime. Sectoral public expenditures do not have, however, a clear effect. A possible

explanation is the following: In the short run public expenditures have no effect (IGS); since public expenditures are increased during Keynesian unemployment periods, we observe an unexpected negative effect (IGS1); finally an effect in the expected direction

emerges after 6 months (IGS2). The sectoral cost of labour indicator (ISB) has significant effects and behaves as an indicator of purchasing power since a stimulus leads to a decrease in the probability of being in the Keynesian unemployment regime and to a

simultaneous increase in the probability of being in the repressed inflation regime. This latter remark actually holds for all sectors. SECTOR 3 Professional equipment

IR IR1 MSD IGS3 0% 0% 14% 0%

ISB

UTP

=

92-7%

(+,+,-,-) (-,o,o,+) IR

IR1

MSD

IGS1

0%

0%

25%

IGS2

IGS3

10%

(+,+,-,-)

ISB

3.79%

(-,0,0,0)

UTP

=

76-8%

0%

(-,0,0,+)

When sectoral public expenditures have significant effects (in general after 9 months: IGS3) they have the expected signs since a stimulus on public expenditures decreases the probability of being in the Keynesian unemployment regime. SECTOR 4

Automobile and transportation IR IR1 IGS1 IGT2 ISN 0% 0-72% 0% 0%

UTP

=

39-3%

(-,0,0,0) (-,0,0,0) (-,0,0,0) IR

IR1 IGS1 IGT2 ISB ISB1 ISN UTP = 0% 4-97% 0 51% 0 94% 6-5% 0.05% (0,0,0,-) (-,0,0,0) (-,0,0,+) (-,0,0,0)

35-7%

Sectoral and total public expenditures (IGS and IGT) are often significant with the correct signs. The indicator of purchasing power ISN plays the expected role since a

stimulus on ISN decreases the probability of being in the Keynesian unemployment regime. SECTOR 5

Consumption goods IR1 IR1 MSD IGT3 0% 0% 0*03% 0%

ISN

UTP=

17%

(+, +,-,-) (-,-, 0, +) (-, O, ,+) IR1

IR1

MSD

0% IR

IGS2

IGS3

IGT2

IGT3

UTP

=

27-6%

0% 0% 004% 39% 1-87% (+,+,-,-) (-,0,-,+) (+,0,+,-) (-,-,0,0)

IR1

0%

MSD

IGS1

IGS2

0%

10%

2-31%

IGS3

ISB

0%

UTP=56

48%

(+, +,-, -) (0, O, O, +) (+, O,0, -)


7%

BOUISSOU ET AL. DISEQUILIBRIUM MICRO ECONOMETRICS 123 In this sector total public expenditures after 9 months (IGT3) and sectoral public expenditures after 6 months (IGS2) have significant effects with the correct signs. Sectoral public expenditures after 9 months (IGS3) have significant effects but with the incorrect

signs. The indicator of purchasing power ISN is strongly significant with the expected signs, while the sectoral real cost of labor indicator ISB is not significant.

5. CONCLUSION This preliminary study has yielded the following results. First, the stability of the results with respect to the various sectors is striking. In all sectors we found that demand surprises

are very significant in explaining the disequilibrium regimes with always the expected

signs. The fact that an increase in public expenditures tends to decrease the probability of being in the Keynesian unemployment regime was clearly shown with a lag of 6 to 9 months. This result does not have, however, the stability of the previous ones. Our

difficulties in obtaining clear estimated effects of public expenditures may be due to the endogeneity of this variable.

The index of purchasing power when significant has the right sign in the sense that

an increase in this variable tends to decrease the probability of being in the Keynesian unemployment regime. We were, however, unable to exhibit the positive impact of an increase in the sectoral wage level on the probability of being in the classical unemployment regime. When this variable is significant it plays the same role as a purchasing power

variable. Finally, we must note that our analysis is hindered by the predominance of the

Keynesian unemployment regime. Our inability to find evidence of the effect of sectoral real wages on the probability of being in the classical unemployment regime may be due

to this characteristic of our sample.

First version received January 1984; final version accepted July 1985 (Eds.)

Support from DRGST 81-E-1303 is gratefully acknowledged. We are indebted to E. Malinvaud and B. Ottenwaelter for giving us access to the individual data collected by INSEE. We are grateful to two anonymous referees and G. Mizon for their remarks on a previous draft. NOTES

1. The possibility of using such surveys for analyzing disequilibria was also suggested by Malinvaud (1981) and Kooiman (1982). 2. For more details on these surveys, see e.g. Bouissou, Laffont, and Vuong (1984). 3. The role of this variable has been emphasized in a macro-disequilibrium framework by Green and Laffont (1981) and in a microeconomic model by Bouissou, Laffont, and Vuong (1984). 4. The same variable was used by Konig, Nerlove, and Oudiz (1981). 5. Two more complex methods of constructing the indicators IQ and IL from the INSEE surveys were tried. For more details, see Bouissou, Laffont, and Vuong (1984). 6. The other result obtained by these authors is a great jump in Keynesian unemployment at the end of 74, i.e. just following the first oil crisis. Though this second result cannot be observed with the present method of constructing IR due to missing data, it can however be observed with the second method of constructing IR that was studied in Bouissou, Laffont, and Vuong (1984). 7. For more details on how these indicators as well as their latent continuous variables were constructed from the series available in the Comptes Nationaux Trimestriels, see Bouissou, Laffont, and Vuong (1984). 8. Alternatively, using the ANOVA constraints (2), it follows that ,u=

(1/KR) EkR log Pr (IRi, = kl IR1 i, IAi,, IBi,, . * .). Thus equation (1) c

tional probabilities in terms of deviations from their log-mean.

9. Any of these assumptions can actually be tested. For instance, Bouissou, Laffont, and Vuong (1985) have derived some readily applicable tests of Assumption A.4 when there are no macro variables Z,.


124 REVIEW OF ECONOMIC STUDIES 10. All our empirical results were obtained by using the program CALM written by J. P. Link. This program estimates conditional ANOVA log-linear probability models (for the theory, see Nerlove and Press (1976), Ottenwaelter and Vuong (1981), Vuong (1982), and for a survey Nerlove (1983)). 11. This test can be thought of as a specification test for the model defined by equation (1). Specifically,

it tests whether restricting effects to bivariate interactions is supported by the data. For formulas giving the appropriate degrees of freedom of the chi-square statistics, see Haberman (1974) and Vuong (1982). 12. In the tables below, if the upper-tail probability is less than 0-005%, it appears as a zero. 13. As mentioned in Section 2, the ANOVA parameterization is used. Since IR has 4 categories, it follows that the (bivariate) effect of an explanatory variable with J categories is characterized by 4 x J ANOVA parameters of which 3 x (J -1) are independent due to the usual ANOVA constraints. Hence, when J =2 it suffices to give the signs of the ANOVA parameters associated with the first category of the dichtomous variable. REFERENCES

ANDERSSEN, E. B. (1973), Conditional Inferences and Modelsfor Measuring. (Copenhagen: Mentalhygiejnisk Forlag).

ARTUS, P., LAROQUE, G. and MICHEL, G. (1984), "Estimation of a Quarterly Macroeconomic Model with Quantity Rationing", Econometrica, 52, 1387-1414.

BOUISSOU, M. B., LAFFONT, J. J. and VUONG, Q. H. (1984), "Econometrie du Desequilibre sur Donnees Microeconomiques", Annales de L'INSEE, 55/56, 109-151.

BOUISSOU, M. B., LAFFONT, J. J. and VUONG, Q. H. (1985), "Tests of Non-Causality under Markov Assumptions on Qualitative Panel Data", Econometrica, (forthcoming). CHAMBERLAIN, G. (1982), "The General Equivalence of Granger and Sims Causality", Econometrica, 50, 569-581.

FAIR, R. C. and JAFFEE, D. M. (1972), "Methods of Estimation of Markets in Disequilibrium", Econometrica, 40, 497-514.

GREEN, J. and LAFFONT, J. J. (1981), "Disequilibrium Dynamics with Inventories and Anticipatory Price Setting", European Economic Review, 16, 199-221.

HABERMAN, S. J. (1974), The Analysis of Frequency Data (Chicago: University of Chicago Press). KONIG, H., NERLOVE, M. and OUDIZ, G. (1981), "On the Formation of Price Expectations: an Analysis of Business Data by Log-Linear Probability Models", European Economic Review, 16, 130-144.

KOOIMAN, P. (1982), "Using Business Surveys Data in Empirical Disequilibrium Models", (ICERD, London School of Economics).

LAFFONT, J. J. (1983), "Fix-Price models: a Survey of Recent Empirical work" (Working Paper No 8305, GREMAQ, Universite des Sciences Sociales de Toulouse).

MALINVAUD, E. (1980), Reexamen de la Theorie du Chomage (Paris: Calman-Levy). MALINVAUD, E. (1981), "Econometric Implications of Macro-Disequilibrium Theory" (mimeo, INSEE). MCFADDEN, D. (1974), "Conditional Logit Analsysis of Qualitative Choice Behavior", in Zarembka, P. (ed) Frontiers in Econometrics (New York: Academic Press).

MUELLBAUER, J. (1978), "Macrotheory versus Macroeconometrics: the Treatment of "Disequilibrium" in Macro Models" (mimeo, Birbeck College).

NERLOVE, M. (1983) "Expectations, Plans, and Realizations in Theory and Practice", Econometrica, 51, 1251-1279.

NERLOVE, M., and PRESS, S. J. (1973) Univariate and Multivariate Log-Linear and Logistic Models (Santa Monica: Rand Corporation).

NERLOVE, M., and PRESS, S. J. (1976), "Multivariate Log-Linear Probability Models for the Analysis of Qualitative Data" (Discussion Paper No 1, Center for Statistics and Probability, Northeastern University). OTTENWAELTER, B. and VUONG, Q. H. (1981), "Modeles Conditionnels log-lineaires de Probabilites et Systemes Recursifs", Annales de l'INSEE, 44, 81-120. QUANDT, R. (1982). "Econometric Disequilibrium Models" (mimeo, Princeton University).

VUONG, Q. H. (1982), "Conditional Log-Linear Probability Models: A Thetretical Development with an Empirical Application" (Unpublished Ph.D. Thesis, Northwestern University). VUONG, Q. H. (1983), "Misspecification and Conditional Maximum Likelihood Estimation" (SSWP No. 503, California Institute of Technology).
